But 18% of voters said they’re still undecided

With Elizabeth Warren and Senator Scott Brown preparing for their second debate Monday night, Warren appears to be inching ahead in the highly competitive race for Senate, as Massachusetts Democrats energized by the presidential race begin to fall in line behind her, according to a new Globe poll.

Warren, a Democrat, leads Brown, a Republican, 43 percent to 38 percent, a shift from the Globe’s last poll in May, when Brown held a 2-point lead. But the race remains within either candidate’s grasp, with 18 percent of voters still undecided, said Andrew E. Smith, the Globe’s pollster and the director of the University of New Hampshire Survey Center.

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This survey is the sixth of eight public polls taken this month that show Warren ahead.

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Warren’s lead is within the poll’s margin of error of plus or minus 4.4 percent, meaning a spread of as much as 8 percentage points between the candidates would still statistically count as a dead heat. Still, the survey is sobering for Brown six weeks before the election.

“It’s trending away from Brown,’’ said Smith. “Brown right now is not doing well enough among Democrats to offset the advantage that Warren has,” said Smith. “That’s just such a big obstacle to overcome for any Republican candidate” in Massachusetts.

Brown’s hurdle is that even as voters from both parties say they like him personally, regard him as bipartisan, and give him high marks on his job performance, many also say they plan to stick with their political party. And in a presidential year, with high turnout expected, that bodes especially well for Democrats on the ballot in Massachusetts. The party holds a 3-to-1 registration advantage over Republicans in the state.

In the presidential contest, the poll shows President Obama leading former governor Mitt Romney by 27 percentage points in Massachusetts, a 57 percent to 30 percent landslide. If that holds up, Brown will face a strong Democratic headwind that could overwhelm his individual efforts as a candidate in the Nov. 6 election.

Of those who said they will vote for Obama, just 9 percent said they also plan to vote for Brown, while 20 percent of Obama voters say they are still undecided in the Senate race, according to the poll.

Romney’s popularity in Massachusetts has plummeted since he won the 2002 governor’s race as a moderate Republican who favored legalized abortion and held other socially liberal stances.

The poll shows 33 percent of respondents view the GOP presidential nominee favorably, compared with 60 percent who viewed him unfavorably, a significant drop since a May poll showed a split among Massachusetts voters on that question. His poor showing in national polls could dampen Republican participation in Massachusetts.

Sampling for the poll of 502 likely voters began the day after the candidates’ first debate, running from Sept. 21 through Sept. 27. Throughout that period, both candidates advertised heavily. They also sparred over Warren’s controversial legal work on behalf of a coal mining company and over a video capturing at least one Brown staff member, along with several from the state Republican Party, engaged in a mock Indian war chant that was criticized as offensive.

After a year of seesawing polls that seemed to show an edge for Brown, a string of polls taken this month have suggested an advantage for Warren.

Charlie Brewer, a 53-year-old self-described independent voter from Franklin, responded to the Globe’s poll saying he was still undecided in the Senate race, though he said he was certain to vote for Obama.

An admirer of what he sees as the senator’s bipartisan spirit, Brewer is the type of voter Brown hopes to win over. But over the last week, since the poll was taken, Brewer said he has made up his mind, in large part because he was turned off by the incident with the Native American chanting. “If it were today, I think the image of those guys whooping with the tomahawk chop, I’d vote for Ms. Warren,” Brewer said.

The Globe poll also shows strong support for two state ballot questions, which require more than 50 percent approval to pass. A full 68 percent of voters, including a majority in both parties, said they support a voter initiative that would make physician-assisted suicide legal for terminally ill patients, compared with 20 percent of respondents who said they oppose the measure. Likewise, 69 percent of voters in the poll said they support a measure to make marijuana legal for medical use. That question also registered bipartisan support.

On the Senate race, the poll suggests that some of Brown’s attacks on Warren may be hurting her credibility. While she remains well liked, 11 percent of voters in the poll described her as dishonest when asked in an open-ended question to offer a one-word description of each candidate.

Brown has continually criticized Warren for listing herself as Native American in a legal directory and in some official documents at universities where she has been employed. She has said her belief in her ancestry, though undocumented, is the result of family lore. She has said the listing did not benefit her career, and numerous people involved in her hiring have backed that up. But she has been unwilling to release personnel records, as Brown has demanded.

The poll suggests most voters are now familiar with the controversy, with 79 percent in the survey saying they were at least somewhat familiar with it, compared with 70 percent who said so in May.

Of those who knew of the controversy, 71 percent said it would have no impact on their vote, while 24 percent said it would make them less likely to support Warren. Notably, 10 percent of Obama’s supporters are among the group who said the controversy makes them less likely to vote for Warren.

John Cunningham, a 43-year-old Democrat from Bellingham who participated in the poll, is one of those voters. “It was just saying to me that, eh, I don’t know if I can really trust this person,” Cunningham said. He said he plans to vote for Obama and for Brown.

Brown has broadened his attacks the last several weeks to include criticism of Warren’s legal work on behalf of two major corporations, Travelers Insurance and LTV Steel, in an attempt to undermine her reputation as a consumer advocate. The poll did not directly ask about those issues, but Smith believes Brown has no choice, from a tactical standpoint, but to go negative, given his need to neutralize Warren’s built-in advantage in party support.

The poll shows no significant backlash so far against Brown for attacking Warren, Smith said, pointing out that when respondents were asked to select the more likable candidate, 58 percent said Brown, compared with 27 percent who chose Warren.

But Warren remains popular for a political newcomer. In a separate question, 53 percent of voters said they view her favorably, compared with 36 percent who view her unfavorably, a ratio that is largely unchanged since May. Warren leads Brown among women by 12 percentage points, a larger margin than the 3-point advantage Brown has with men.

Though Warren has been attacking Brown as unreliable on women’s issues, more than half of voters, including a plurality of Democrats, view him as supportive of issues that are important to female voters.